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Imagine a current flowing through a wire connected between a negative terminal on the left and a positive terminal on the right. Through the wire, millions of electrons are flowing from left to right.
Each electron carries a charge of 1.6E–19 coulombs. Let's say we observe a current of 1 μA, in which case 7.8E12 electrons pass every second. If the interval between electrons were the same, then at 7800 GH, we would see a ripple like the teeth of a saw blade moving at high speed.
Shot Noise in P-N Junctions
But in a diode or a bipolar transistor, we see a very different effect. Here, the current is initiated by electrons and holes moving across a barrier. This movement is anything but smooth: within any given time interval, one electron or hole may cross the barrier, or five, or 100, or none. The variation is so great that there is no discernable peak at 7800 GHz or, for that matter, any other frequency.
In fact, because of the very large number of electrons, this shot noise is so well distributed over the frequency range that it has a constant level over the entire spectrum:
$$I_{noise(RMS)} ~=~ \sqrt {2qIB}$$
where:
q = electron charge (1.6E–19 coulombs)
I = DC current
B = bandwidth in Hz
Because the shot noise is constant at all frequencies, it is considered a white noise. There are two things you should notice here:
- Noise increases as the square root of bandwidth.
- Decreasing the current increases the ratio of the noise to the current.
To illustrate this second point, Table 1 compares the noise at three different current levels, assuming a 10 kHz bandwidth.
Table 1. Comparison of shot noise current at different DC current levels
| DC Current | Noise Current | Ratio of Currents (%) | Ratio of Currents (dB) |
| 10 mA | 1.8 nARMS | 0.00018% | -115 |
| 1 μA | 57 pARMS | 0.0057% | -85 |
| 10 mA | 1.8 pARMS | 0.18% | -55 |
All of this shows that it’s harder to design a low-noise circuit at low current levels.
Johnson Noise
There is also noise when no current flows at all. Using the energy imparted by temperature, some electrons will suddenly leave an orbit and jump to another orbit. The higher the temperature, the larger this irregularity becomes.
Because of this, a resistor actually has a noise voltage at its terminals, even when doing nothing but lying on a bench. We refer to this as the Johnson noise. It’s calculated as follows:
$$V_{noise(RMS)} ~=~ \sqrt {4kTRB}$$
where:
k = the Boltzmann constant, 1.38E–23 joules/T)
T = the temperature in Kelvin
R = the resistance
B = the bandwidth.
For example, a 1 MΩ resistor always has a noise voltage of 13 μVRMS at room temperature if measured over a bandwidth of 10 kHz. Johnson noise is also referred to as thermal noise or Nyquist noise.
Whenever you mention a noise voltage or current, you also have to state the bandwidth. To avoid this requirement, noise voltage is often expressed in nV/√Hz (nanovolts per root-hertz). To get the real noise voltage, you simply multiply this value by the square root of the bandwidth.
Flicker Noise
Shot noise and Johnson noise are fundamental—they’re present in any current or resistor. There’s also another type of noise that, while not exactly fundamental, is always present. It’s called 1/f noise or flicker noise.
Flicker noise is worst in MOS transistors, which is a major reason why bipolar transistors are preferred in low-noise analog applications. The silicon oxide interface is capable of holding some electrons for a considerable period (seconds) and then releasing them in bunches.
At low frequencies, the flicker noise increases to far above the white-noise level. At 1 Hz, the noise level (in nV/√Hz) can be two orders of magnitude higher than at 1 MHz.
Flicker noise is also present in bipolar devices, but to a lesser extent.
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